how to find the sum of the interior angles of a polygon
Answers
Answered by
3
Answer:
n-2×180 (in which n is the number of sides)
Answered by
3
One Interior Angle
Now, what about the measure of just one of the interior angles? What do you think we would need to do to find the measure of just one angle if we already know how to find the sum of their measures and that for a regular polygon all the angles are equal? Yes, we would need to divide our sum by the number of sides we have. And that is what our formula tells us to do.
Measure of Interior Angle = (n - 2) * 180 / n
Let's go back to our triangle. We know that an equilateral triangle, a regular triangle, has all of its angles measuring 60 degrees. So, does this check out with our formula? Let's find out. Our regular polygon is a triangle with 3 sides, so our n equals 3. We plug that into our equation, and we get (3 - 2) * 180 / 3 = 1 * 180 / 3 = 180 / 3 = 60. Look at that! It works, too!
Likewise, with the sum of the measure of interior angles, we can use this to find the measure of any interior angle of any regular polygon. All we need to do is to plug in our number of sides into the equation.
Similar questions